1860 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY 2017

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1 1860 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY 2017 Correspondence Near-Optima Signa Detector Based on Structured Compressive Sensing for Massive SM-MIMO Zhen Gao, Lingong Dai, Chenhao Qi, Chau Yuen, and Zhaocheng Wang Abstract Massive spatia-moduation mutipe-input mutipe-output SM-MIMO with high spectrum efficiency and energy efficiency has recenty been proposed for future green communications. However, in massive SM-MIMO, the optima maximum-ikeihood detector has the high compexity, whereas state-of-the-art ow-compexity detectors for sma-scae SM-MIMO suffer from an obvious performance oss. In this paper, by expoiting the structured sparsity of mutipe SM signas, we propose a ow-compexity signa detector based on structured compressive sensing SCS to improve the signa detection performance. Specificay, we first propose the grouped transmission scheme at the transmitter, where mutipe SM signas in severa continuous time sots are grouped to carry the common spatia consteation symbo to introduce the desired structured sparsity. Accordingy, a structured subspace pursuit SSP agorithm is proposed at the receiver to jointy detect mutipe SM signas by everaging the structured sparsity. In addition, we aso propose the SM signa intereaving to permute SM signas in the same transmission group, whereby the channe diversity can be expoited to further improve signa detection performance. Theoretica anaysis quantifies the gain from SM signa intereaving, and simuation resuts verify the near-optima performance of the proposed scheme. Index Terms Massive mutipe-input mutipe-output MIMO, signa detection, signa intereaving, spatia moduation SM, structured compressive sensing SCS. I. INTRODUCTION SPATIAL-MODULATION mutipe-input mutipe-output SM- MIMO expoits the pattern of one or severa simutaneousy active antennas out of a avaiabe transmit antennas to transmit extra information [1], [2]. Compared with sma-scae SM-MIMO, which ony introduces the imited gain in spectrum efficiency, massive SM-MIMO has recenty proposed by integrating SM-MIMO with massive MIMO working at 3 6 GHz to achieve higher spectrum efficiency [1]. In massive SM-MIMO systems, the base station BS uses Manuscript received Apri 8, 2015; revised October 17, 2015 and January 26, 2016; accepted March 31, Date of pubication Apri 21, 2016; date of current version February 10, This work was supported in part by the Nationa Natura Science Foundation of China under Grant and Grant , by the Internationa Science and Technoogy Cooperation Program of China under Grant 2015DFG12760, by the Singapore A STAR Project under Grant , and by the Beijing Natura Science Foundation under Grant The review of this paper was coordinated by Dr. Y. Ma. Z. Gao, L. Dai, and Z. Wang are with the Tsinghua Nationa Laboratory for Information Science and Technoogy, Department of Eectronic Engineering, Tsinghua University, Beijing , China e-mai: gao-z11@mais.tsinghua. edu.cn; dai@mai.tsinghua.edu.cn; zcwang@mai.tsinghua.edu.cn. C. Qi is with the Schoo of Information Science and Engineering, Southeast University, Nanjing , China e-mai: qch@seu.edu.cn. C. Yuen is with Singapore University of Technoogy and Design, Singapore e-mai: yuenchau@sutd.edu.sg. Coor versions of one or more of the figures in this paper are avaiabe onine at Digita Object Identifier /TVT a arge number of ow-cost antennas for higher spectrum efficiency but ony one or severa power-hungry transmit radio frequency RF chains to save power, whereas the user can compacty empoy the mutipe receive diversity antennas with ow correation [2]. Since the power consumption and hardware cost are argey dependent on the number of simutaneousy active transmit RF chains particuary the power ampifier, massive SM-MIMO outperforms the traditiona MIMO schemes in higher spectrum efficiency, reduced power consumption, ower hardware cost, etc. In practice, SM can be adopted in conventiona massive MIMO systems as an energy-efficient transmission mode. Meanwhie, massive SM-MIMO can be aso considered as an independent scheme to reduce both power consumption and hardware cost. For massive SM-MIMO, due to the sma number of receive antennas at the user and massive antennas at the BS, the signa detection is a chaenging arge-scae underdetermined probem. When the number of transmit antennas becomes arge, the optima maximum ikeihood ML signa detector suffers from the prohibitivey high compexity [3]. Low-compexity signa vector SV-based detector has been proposed for SM-MIMO [3], but it is confined to SM-MIMO with a singe transmit RF chain. In [4] [6], the SM is generaized, where more than one active antennas are used to transmit independent signa consteation symbos for spatia mutipexing. Linear minimum mean square error LMMSE-based signa detector [1] and sphere decoding SD-based detector [7] can be used for SM-MIMO systems with mutipe transmit RF chains. However, they are ony suitabe for we or overdetermined SM-MIMO with N r N t and suffer from a significant performance oss in underdetermined SM-MIMO systems with N r <N t,wheren t and N r are the numbers of transmit and receive antennas, respectivey. Due to a imited number of RF chains, SM signas have the inherent sparsity, which can be considered by expoiting the compressive sensing CS theory [8] for improved signa detection performance. By far, CS has been widey used in wireess communications [9] [12], and the CS-based signa detectors have been proposed for underdetermined sma-scae SM-MIMO [11], [12]. However, their bit-error-rate BER performance sti has a significant gap compared with that of the optima ML detector, particuary in massive SM-MIMO with arge N t, N r,andn r N t. This paper proposes a near-optima structured compressive sensing SCS-based signa detector with ow compexity for massive SM- MIMO. Specificay, we first propose the grouped transmission scheme at the BS, where mutipe successive SM signas are grouped to carry the common spatia consteation symbo to introduce structured sparsity. Accordingy, we propose a structured subspace pursuit SSP agorithm at the user to detect mutipe SM signas, whereby their structured sparsity is everaged for improved signa detection performance. Moreover, the SM signa intereaving is proposed to permute SM signas in the same transmission group, so that the channe diversity can be expoited. Theoretica anaysis and simuation resuts verify that the proposed SCS-based signa detector outperforms existing CSbased signa detector. Notation: Bodface owercase and uppercase symbos represent coumn vectors and matrices, respectivey. denotes the integer foor operator. The transpose, conjugate transpose, and Moore Penrose matrix inversion operations are denoted by T,,and, respectivey. The p -norm operation is given by p,and denotes the IEEE. 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2 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY Fig. 1. Spatia consteation symbo and the signa consteation symbo in SM-MIMO systems, where N t = 4, N a = 1, and QPSK are considered an exampe. cardinaity of a set. E{ }, var{ }, Re{ }, andim{ } are operators to take the expectation, variance, the rea part, and the imaginary part of a random variabe. Tr{ } is the trace operation for a matrix. If a set has n eements, the number of k-combinations is denoted by the binomia coefficient n k. The index set of nonzero entries of the vector x is caed the support set of x, which is denoted by supp{x}, x i denotes the ith entry of the vector x,andh i denotes the ith coumn vector of the matrix H. x Γ denotes the entries of x defined in the set Γ, whereas H Γ denotes a submatrix of H with indexes of coumns defined by the set Γ. II. SYSTEM MODEL In SM-MIMO systems, the transmitter has N t transmit antennas but N a <N t transmit RF chains, and the receiver has N r receive antennas. Each SM signa consists of two symbos see Fig. 1: the spatia consteation symbo obtained by mapping og Nt 2 N a bits to a pattern of N a active antennas out of N t transmit antennas and N a independent signa consteation symbos coming from the M-ary signa consteation set e.g., quadrature ampitude moduation. Hence, each SM signa carries the information of N a og 2 M + og Nt 2 N a bits. At the receiver, the received signa y C Nr 1 can be expressed as y = Hx + w, where x C Nt 1 is the SM signa transmitted by the transmitter; w C Nr 1 is the additive white Gaussian noise AWGN vector with independent and identicay distributed i.i.d. entries foowing the circuar symmetric compex Gaussian distribution CN0,σw; 2 H = R 1/2 1/2 r HR t C Nr Nt is the correated fat Rayeigh-fading MIMO channe, with entries of H being subjected to the i.i.d. distribution CN0, 1; andr r and R t are the receiver and transmitter correation matrices, respectivey [13]. The correation matrix R is given by r ij = r i j,wherer ij is the ith row and the jth coumn eement of R, andr is the correation coefficient of neighboring antennas. It shoud be pointed out that H shoud be known by the receiver and can be acquired by channe estimation [13]. To achieve both high spectrum efficiency and energy efficiency, massive SM-MIMO, which empoys massive ow-cost antennas but few power-hungry transmit RF chains at the BS to serve the user with comparativey sma number of receive antennas, has recenty been proposed [1]. However, its signa detection is a chaenging arge-scae underdetermined probem since N t,n r can be arge and N r N t, e.g., N t = 64 and N r = 16 are considered [1]. For x, the spatia consteation symbo of og 2 Nt N a bits is mapped into the spatia consteation set A, where the pattern of N a active antennas seected from N t transmit antennas is regarded as the spatia consteation symbo. Hence, there are A = 2 og 2 N t Na kinds of patterns of active antennas, i.e., supp{x} A. Meanwhie, the signa consteation symbo of the ith active antenna, which is denoted by x i for 1 i N a, is mapped into the M-ary signa consteation set B. Therefore, the signa detection in SM-MIMO can be formuated as the M Na 2 og 2 N t Na -hypothesis detection probem. Ceary, the optima signa detector to this probem is the ML signa detector, which can be expressed as [1] ˆx ML =arg min y Hx 2. 1 suppx A,x i B,1 i N a However, the computationa compexity of the optima ML signa detector is OM Na 2 og 2 N t Na, which can be unreaistic when N t, N a, and/or M become arge. To reduce the compexity, the SV-based signa detector has been proposed [3], but it ony considers the case of N a = 1. The LMMSE-based signa detector with the compexity of O2N r Nt 2 + Nt 3 [1] and the SD-based signa detector with the compexity of Omax{Nt 3,N r Nt 2,Nr 2 N t } [7] have been proposed for we or overdetermined SM-MIMO with N r N t. However, for underdetermined SM-MIMO systems with N r <N t, these detectors suffer from a significant performance oss [12]. Since ony N a transmit antennas are active in each time sot for power saving and ow hardware cost, there are ony N a <N t nonzero entries in x; thus, the SM signa has the inherent sparsity. By expoiting such sparsity, the CS-based signa detectors have been proposed for SM [10] [12]. In [10], a spatia moduation matching pursuit SMMP agorithm is proposed to detect mutiuser SM signas in the upink massive SM-MIMO systems. In [11] and [12], the CS-based signa detectors are proposed for underdetermined singe-user SM-MIMO systems with N r <N t in the downink. The normaized compressive sensing NCS detector with the compexity of O2N r Na 2 + Na 3 in [11] first normaizes the MIMO channes and then uses orthogona-matching-pursuit agorithm to detect signas. In [12], a basis pursuit denoising BPDN agorithm with the compexity of ONt 3 from the cassica basis pursuit agorithm is deveoped to detect SM signas. However, both NCS and BPDN detectors are based on the framework of CS theory, and such CS-based signa detectors sti suffer from a significant performance gap compared with the optima ML detector when N t /N r becomes arge, particuary in massive SM-MIMO systems with N r N t [12]. III. PROPOSED STRUCTURED COMPRESSIVE SENSING-BASED SIGNAL DETECTOR In this section, an SCS-based signa detector is proposed for downink singe-user massive SM-MIMO as shown in Fig. 2. A. Grouped Transmission and Intereaving at the Transmitter We assume that signa consteation symbos in the proposed scheme are mutuay independent. Moreover, for the proposed grouped transmission scheme, every G consecutive SM signas are considered as a group, and SM signas in the same transmission group share the same spatia consteation symbo, i.e., supp x 1 = supp x 2 = = supp x G 2 where x 1, x 2,...,x G are SM signas in G consecutive time sots. Due to the conveyed common spatia consteation symbo, x 1, x 2,...,x G in the same transmission group share the same support set and thus have the structured sparsity. It is cear that to introduce such structured sparsity, the effective information bits carried by spatia consteation symbos wi be reduced. However, as wi be demonstrated in our simuations, such structured sparsity

3 1862 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY 2017 Fig. 2. Proposed SCS-based signa detector, where N t = 4, N r = 2, N a = 1, G = 2, and QPSK are considered. Note that the white dot bock in MIMO channes denotes the deep channe fading. aows more reiabe signa detection performance and eventuay coud even improve the BER performance of the whoe system without the reduction of the tota bit per channe use bpcu. On the other hand, due to the tempora channe correation, channes in severa consecutive time sots can be considered to be quasi-static, i.e., H 1 = H 2 = = H G,whereH t for 1 t G is the channe associated with the tth SM signa in the group. This impies that if channes used for SM fa into the deep fading, such deep fading usuay remains unchanged during G time sots, and the corresponding signa detection performance wi be poor. To sove this issue, we further propose the SM signa intereaving at the transmitter. Specificay, after the origina SM signas x t s are generated, the actuay transmitted signas are given by Π t x t s, where each coumn and row of Π t C Nt Nt ony has one nonzero eement with the vaue of one, and Π t can permutate the entries in x t. We consider that Π t s for 1 t G are different in different time sots, and they are predefined and known by both the transmitter and receiver. In this way, the active antennas vary in different time sots from the same transmission group, athough x t s share the common spatia consteation symbo. Hence, the channe diversity can be appropriatey expoited to improve the signa detection at the receiver. In Section IV-B, such diversity gain wi be further discussed. B. SCS-Based Signa Detector at the Receiver At the receiver, the received signa in the tth time sot is y t = H t Π t x t + w t = H t x t + w t 3 where H t = H t Π t is the deintereaving processing. From 3, we observe that x t s share the structured sparsity, but they have different nonzero vaues. According to SCS theory, the structured sparsity of x t s can be expoited to improve the signa detection performance compared with the conventiona CS-based signa detectors [8]. Under the framework of SCS theory, the soution to 3 can be achieved by soving the foowing optimization probem: G 1 q x t q p min suppx t A s.t. y t = H t x t, supp x t = supp x 1 t. 4 In this paper, based on the cassica subspace pursuit SP agorithm [8], we propose an SSP agorithm by utiizing the structured sparsity to sove the optimization probem 4 in a greedy way, where p = 0 and q = 2 are advocated [8]. The proposed SSP agorithm is described in Agorithm 1. Specificay, Lines 1 3 perform the initiaization. In the kth iteration, Line 5 performs the correation between the MIMO channes and the residua in the previous iteration; Line 6 obtains the potentia true indexes according to Line 5; Line 7 merges the estimated indexes obtained in Lines 8 9 in the previous iteration and the estimated indexes in Line 6 in the current iteration; after the east squares in Line 8, Line 9 removes wrong indexes and seects N a most ikey indexes; Line 10 estimates SM signa according to Ω k ;andline 11 acquires the residue. The iteration stops when k>n a. Compared with the cassica SP agorithm that ony reconstructs one sparse signa from one received signa, the proposed SSP agorithm can jointy recover mutipe sparse signas with the structured sparsity but having different measurement matrices, where the structured sparsity of mutipe sparse signas can be everaged for improved signa detection performance. Therefore, the cassica SP agorithm can be regarded as a specia case of the proposed SSP agorithm when G = 1, and more detais wi be discussed in Section IV-A. Another difference shoud be pointed out that in the steps of Lines 6 and 9 in Agorithm 1, the seected support set shoud beong tothe predefined spatia consteation set A for enhanced signa detection performance. However, the cassica SP agorithm and existing CS-based signa detectors do not expoit such priori information of the expected support set [11], [12]. By using the proposed SSP agorithm, we can acquire the estimation of the spatia consteation symbo according to suppˆx t s and the rough estimation of signa consteation symbos. By searching for the minimum Eucidean distance between the rough estimation of signa consteation symbos and egitimate consteation symbos, we can finay estimate signa consteation symbos. Agorithm 1 Proposed SSP Agorithm. Input: Received signa y t, the channe matrix H t, and the number of active antennas N a,where1 t G. Output: Estimated SM signa ˆx t for 1 t G. 1: Ω 0 = ; 2: r t = y t t; 3: k = 1; 4: whie k N a do 5: a t =H t r t t; 6: Γ=arg max{ G Γ Γ 2, Γ A, Γ =min{2n a,n r } 2 if k = 1or Γ =min{n a,n r N a } if k>1}; 7: Ξ=Ω k 1 Γ; 8: b t Ξ =H t Ξ y t t; 9: Ω k =argmax{ G Ω Ω 2, Ω A and Ω =N a }; 2 10: c t =H t y t Ω k Ω k t; 11: r t = y t H t c t t; 12: k = k + 1; 13: end whie 14: ˆx t = c t t;

4 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY IV. PERFORMANCE ANALYSIS In this section, we wi provide the performance anaysis. A. Comparison of SCS-Based and CS-Based Signa Detectors Typicay, existing CS-based signa detectors utiize one received signa vector to recover one sparse SM signa vector, which is a typica singe measurement vector SMV probem, i.e., y = Hx + w. If mutipe sparse signas share the common support set and identica measurement matrix, i.e., [y 1, y 2,...,y G ]= H[x 1, x 2,...,x G ]+w, the reconstruction of x t s from y t s for 1 t G can be considered as the mutipe-measurementvector MMV probem in SCS theory [8]. The SCS theory has proven that with the same size of the measurement vector, the recovery performance of SCS agorithms is superior to that of conventiona CS agorithms [8]. This impies that with the same number of receive antennas N r, the proposed SCS-based signa detector can outperform conventiona CS-based signa detectors. Compared with the conventiona MMV probem, our formuated probem 4 is to sove mutipe sparse signas with the common support set but having different measurement matrices. Hence, both conventiona SMV probem and MMV probem can be considered the specia cases of our probem. If Π t s are identica, 4 becomes the conventiona MMV probem, and furthermore, if G = 1, it reduces to the SMV probem. Therefore, our formuated probem can be regarded as a generaized MMV GMMV probem. B. Performance Gain From SM Signa Intereaving We discuss the performance gain from the SM signa intereaving by comparing the detection probabiity of the proposed SSP agorithm with and without SM signa intereaving. Here, we consider a simpified scenario with N a = 1 and uncorreated Rayeigh-fading MIMO channes. Let m be the index of the active antenna, and for any given, H t s for 1 t G are mutuay independent, where 1 m, N t. Based on these assumptions, the received signa is given by y t = α t H t m + wt,for1 t G, whereα t B denotes the signa consteation symbo carried by the active antenna in the tth time sot. To identify the active antenna, the proposed SSP agorithm reies on the correation operation in Line 5 of Agorithm 1, i.e., G C y t H t G 2 = α t H t m + w t H t 2 = G F t m, 2 5 where F t m, =αt H t m + w t H t for 1 N t. Due to arge N r in practice, we have Re{F m,m} t Nμ 1,σ1 2 with μ 1 = 0, σ1 2 =Nr 2 + N r σs/2 2 δm = 2 + N r σw/2, 2 and Im{F m,m} t Nμ 2,σ2 2 with μ 2 = 0, σ2 2 =1 δm = 2 Nr 2 + N rσs 2/2+N rσw 2 /2 according to centra imit theorem [14]. Simiary, both Re{F t t m, } and Im{F m, } foow the distribution N μ 3,σ3 2 with m, μ 3 =0, and σ3 2 =N rσs 2/2+N rσw 2 /2.Note that σ 2 s =Tr{E{xt x t T }}, andre{f t m, t } and Im{F m, } are mutuay independent. Moreover, we can have C m σ2χ 2 2 G + σ1χ 2 2 G and C σ3χ 2 2 2G with m, whereχ2 n is the centra chi-squared distribution with the degrees of freedom n [14]. Since Agorithm 1 ony has one iteration and Γ = Ξ = 2 in the iteration for N a = 1, we consider P GMMV C m C [2] antenna detection probabiity, where C [1] > 0 m as the correct active >C [2] > >C [Nt Na] with m are sequentia statistics. The probabiity density functions pdfs of C m and C with m are denoted by f 1 x and f 2 x, respectivey. The pdf of C [2] with m is f [2] 2 x= N t N a!/n t N a 2!F 2 x Nt Na 2 1 F 2 xf 2 x, where F 2 x is the cumuative density function of f 2 x.inthisway,wehave P GMMV C m C [2] > 0 m = 0 fxf [2] 2 x zdxdz. 6 For the conventiona MMV probem with identica channe matrices, simiar to the previous anaysis, we have C m Gσ2 2χ2 1 + Gσ1χ and C Gσ3χ with m. Simiary, we can aso get > 0 m. To intuitivey compare the signa detection probabiity, we compare P MMV C m C > 0 m and P GMMV C m C > 0 m when σs/σ 2 w 2 and G are sufficient arge. In this case, C m C can be approximated to the Gaussian distribution N μ 4,σ4 2 with μ 4 = Gμ μ 2 2 2μ σ1 2 + σ2 2 2σ3, 2 σ4 2 = P MMV C m C [2] G 3 i=1 2σ4 i + 4μ 2 i σi 2. In this way, we can obtain that P GMMV C m C > 0 m Q μ 4 /σ 4,whereQ-function is the tai probabiity of the standard norma distribution [14]. By contrast, for the conventiona MMV case, we can obtain that P MMV C m C > 0 m Q μ 4 / Gσ 4. Ceary, P MMV is arger than P GMMV due to μ 4 > 0andG>1, which impies that an appropriate SM signa intereaving wi ead to the improved signa detection performance. s, are mutuay independent, we consider the pseudorandom permutation matrix Π t. In Section V, simuation resuts confirm the good channe diversity gain from intereaving, whose performance gain approaches that of the case of mutuay independent channe matrices in the same group. To achieve the goa that H t C. Computationa Compexity The optima ML signa detector has the compexity of OM Na 2 og 2 N t Na, which is high for arge N a, N t, and/or M. The conventiona signa detectors [1], [7], [12] have the compexity of ONt 3, which is sti high in massive SM-MIMO systems with arge N t. By contrast, for the proposed signa detector, the main computationa burden comes from the step of east squares with the compexity of OG2N r Na 2 + N a 3 [8], or equivaenty O2N r Na 2 + Na 3 per SM signa in each time sot. This indicates that the proposed SCS-based signa detector enjoys the same order of compexity with the CS-based signa detector [11]. V. S IMULATION RESULTS A simuation study was carried out to compare the performance of the proposed SCS-based signa detector with that of the conventiona LMMSE-based signa detector [1] and the CS-based signa detector [12]. The performance of the optima ML detector [6] is aso provided as the benchmark for comparison. Fig. 3 compares the simuated and anaytica spatia consteation symbo error rate SCSER of the SCS-based signa detector in different cases over uncorreated Rayeigh-fading MIMO channes, where N t = 64, N r = 16, N a = 1, and 8-phase-shift keying PSK are considered. For the GMMV case, i.i.d. denotes the case that H t = H t t and H t s are independenty generated, whereas intereaving denotes the case that H 1 = H 2 = = H G and H t = H t Π t with different permutation matrices Π t s.ceary,the anaytica SCSER derived in Section IV-B have the good tightness with the simuation resuts. In addition, the proposed SCS-based signa

5 1864 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY 2017 Fig. 3. Comparison of the simuated and anaytica SCSER of the SCS-based signa detector in different cases over uncorreated Rayeigh-fading MIMO channes, where N t = 64, N r = 16, N a = 1, and 8-PSK are considered. Fig. 5. BER comparison between the traditiona CS-based signa detector and the proposed SCS-based signa detector over correated Rayeigh-fading MIMO channes, where r t = r r = 0.4 and N r = 16 are considered. Fig. 4. SCSER of different signa detectors over correated Rayeigh-fading MIMO channes, where r t = r r = 0.4, N t = 64, N r = 16, N a = 1, and 8-PSK are considered. Fig. 6. BER performance comparison between the proposed SCS-based signa detector and the optima ML signa detector, where r t = r r = 0.4, N t = 65, N r = 16, N a = 2, and 8-PSK are considered. detector outperforms the conventiona CS-based signa detector since the structured sparsity of mutipe sparse SM signas is expoited. Moreover, since the channe diversity can be aso expoited, the SCSbased signa detector with mutuay independent channe matrices is superior to that with identica channe matrices by more than 4 db if the SCSER of 10 3 is considered. Finay, the performance of the SCS-based signa detector with SM signa intereaving approaches that with mutuay independent channe matrices, which indicates that the proposed SM signa intereaving can fuy expoit the channe diversity. Fig. 4 provides SCSER comparison of different signa detectors over correated Rayeigh-fading MIMO channes, where both the channe correation coefficients at the transmitter and receiver are r t = r r = 0.4 [13], N t = 64, N r = 16, N a = 1, and 8-PSK are considered. The conventiona LMMSE-based signa detector works poory due to N r N t. The SCS-based signa detector with intereaving outperforms the conventiona CS-based signa detector and SCS-based signa detector without intereaving. Moreover, it has the simiar performance with that with mutuay independent channe matrices i.e., H t = H t t and H t s are independenty generated, which indicates the good channe diversity gain from intereaving, even in correated MIMO channes. Fig. 5 provides the BER performance comparison of the existing CS-based signa detector and the proposed SCS-based signa detector with intereaving over correated Rayeigh-fading MIMO channes with r t = r r = 0.4 and N r = 16. The existing scheme adopts two transmission modes: 1 N t = 64, N a = 1, and binary PSK with 7 bpcu; and 2 N t = 65, N a = 2, and no signa consteation symbo with 11 bpcu. In contrast, the SCS-based signa detector with N t = 65, N a = 2, and G = 2 adopts quadrature PSK and 8-PSK, respectivey, and the corresponding data rates are 9.5 and 11.5 bpcu. In Fig. 5, it can be observed that the proposed SCS-based signa detector with even higher bpcu achieves better BER performance than the conventiona CS-based signa detector. Fig. 6 compares the performance of the proposed SCS-based signa detector with intereaving and the optima ML signa detector, where r t = r r = 0.4, N t = 65, N r = 16, N a = 2, and 8-PSK are considered. We find that with the increasing G, the BER performance gap between the SCS-based signa detector and the optima ML signa detector becomes smaer. When G 2, the SCS-based signa detector approaches the optima ML signa detector with a sma performance oss. For exampe, if the BER of 10 4 is considered, the performance gap between the SCS-based signa detector with G = 3 and the optima ML detector is ess than 0.2 db. Thus, the nearoptima performance of the proposed SCS-based signa detector can be verified.

6 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY VI. CONCLUSION This paper has proposed a near-optima SCS-based signa detector with ow compexity for the massive SM-MIMO. First, the grouped transmission scheme can introduce the desired structured sparsity of mutipe SM signas in the same transmission group for improved signa detection performance. Second, the SSP agorithm can jointy detect mutipe SM signas with ow compexity. Third, by using SM signa intereaving, we can fuy expoit the channe diversity to further improve the signa detection performance, and the gain from SM signa intereaving can approach that of the idea case of mutuay independent channe matrices in the same transmission group. Moreover, we have quantified the gain from SM signa intereaving. Simuation resuts have confirmed the near-optima performance of the proposed scheme. REFERENCES [1] M. Di Renzo, H. Haas, A. Ghrayeb, S. Sugiura, and L. 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Haas, Channe estimation for spatia moduation, IEEE Trans. Commun., vo. 62, no. 12, pp , Dec [14] S. M. Kay, Fundamentas of Statistica Signa Processing, Voume II: Detection Theory. Upper Sadde River, NJ, USA: Prentice-Ha, Performance Anaysis of Neighbor Discovery Process in Buetooth Low-Energy Networks Wha Sook Jeon, Senior Member, IEEE, Made Harta Dwijaksara, and Dong Geun Jeong, Senior Member, IEEE Abstract To support various Internet of Things IoT appications, the Buetooth Low Energy BLE standard specifies a wide range of parameter vaues for the neighbor discovery process NDP. The parameter vaues used during neighbor discovery directy affect the performance of the NDP. Therefore, an optima parameter setting is essentia to achieve the best tradeoff between discovery atency and energy consumption. An anaytica mode can offer a beneficia guideine for such a parameter seection. In this paper, we propose a genera mode for anayzing the performance of NDP in BLE networks. In the mode, the operations of the scanner and the advertiser, which are two main components of NDP, are expressed on the discrete-time axis. Based on the Chinese Remainder Theorem CRT, the discovery atency and energy consumption of advertiser are derived. The numerica resuts from our mode are amost the same as the simuation resuts, for any parameter vaues specified by the standard. When considering that BLE is one of candidate communication technoogies for IoT, the proposed mode is expected to be very usefu in setting the defaut or initia vaues of NDP parameters for various IoT appications. Index Terms Buetooth Low Energy BLE, discovery atency, energy consumption, Internet of Things IoT, neighbor discovery. I. INTRODUCTION Buetooth ow energy BLE, which is a compementary technoogy of cassic Buetooth and is targeting utra-ow-power and ow-cost communication, has attracted much attention recenty as one of the key enabing technoogies for the Internet of Things IoT [1]. To design an utra-ow-power BLE system, some major modifications were made to the cassic Buetooth, one of which was for the neighbor discovery process NDP [2]. A communications in BLE networks must invove NDP in the first pace since it enabes a BLE device to set up a connection or exchange information with its neighbors. Therefore, it is very desirabe to have a fast and energy-efficient NDP. To this end, unike cassic Buetooth which may use a the avaiabe channes for discovery purposes, BLE dedicates ony three specia channes caed advertising channes to neighbor discovery. Note that fewer advertising channes ead to fast discovery and this can give the devices more chances to put their transmitter/receiver eectronics into seep. In addition, BLE adopts more reaxed timing for NDP so that a device can fexiby contro its duty cyce during NDP. The timing is determined by severa discovery parameters of which vaues directy affect the NDP performance. The BLE standard specifies a wide range of feasibe parameter vaues for NDP, to support Manuscript received February 1, 2015; revised August 2, 2015 and December 11, 2015; accepted Apri 13, Date of pubication Apri 25, 2016; date of current version February 10, This work was supported by the Nationa Research Foundation of Korea funded by the Korean Government MSIP under Grant 2015R1A5A The review of this paper was coordinated by Dr. M. Dianata. W. S. Jeon and M. H. Dwijaksara are with the Department of Computer Science and Engineering, Seou Nationa University, Seou , South Korea e-mai: wsjeon@snu.ac.kr; made.harta@mcc.snu.ac.kr. D. G. Jeong is with the Department of Eectronics Engineering, Hankuk University of Foreign Studies, Yongin , Korea e-mai: dgjeong@hufs. ac.kr. Coor versions of one or more of the figures in this paper are avaiabe onine at Digita Object Identifier /TVT IEEE. Persona use is permitted, but repubication/redistribution requires IEEE permission. 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